The "Dispel magic" descriptor states that "the effect of a spell with an instantaneous duration can't be dispelled, because the magical effect is already over before the dispel magic can take effect", however does dispel magic work (ie repress the magic of the item for 1d4 rounds) on a magical item whose imbued spell is of the instantaneous duration type?

As a more tangible example, an Eberron Airship is created by binding a wind elemental to the ship using the planar binding spell (duration: instantaneous) and Bind Elemental item creation feat. Would casting "dispel magic" halt the airship for 1d4 rounds?

2 Answers
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Normally, any magic item created with an instantaneous spell is subject to dispel magic as normal. The spell is used up as part of the item creation, and any dispel attempts must be made against the item, not the spell.

However, the Bind Elemental feat is a special case:

All bound-elemental items have a planar binding spell as a prerequisite, but simply casting the spell as part of the item creation is not sufficient. You must cast the spell normally, using the item that is to hold the elemental and a Khyber dragonshard as a receptacle.

Thus the elemental binding isn't affected by dispel magic, since that spell is separate to the usual item creation process. The item itself can still be dispelled, in which case it is suppressed for 1d4 rounds as normal, but the elemental remains bound.

As an aside, conjuration spells have explicit rules on whether created objects are magic or not. Amusingly they imply that the Orb of Force spell creates a permanent and nonmagical force object.
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starwedSep 16 '12 at 21:48

If the object that you target is a magic item, you make a dispel check against the item’s caster level. If you succeed, all the item’s magical properties are suppressed for 1d4 rounds, after which the item recovers on its own. A suppressed item becomes nonmagical for the duration of the effect. An interdimensional interface (such as a bag of holding) is temporarily closed. A magic item’s physical properties are unchanged: A suppressed magic sword is still a sword (a masterwork sword, in fact). Artifacts and deities are unaffected by mortal magic such as this.

I am not familiar with the item you are talking about, and have only played in one Eberron campaign. But unless Eberron has radically different magic rules I'm unaware of, you'll still be running with a dispel check against the caster level of the item. Even wands of magic missile can be suppressed in this way, an instantaneous spell effect.

On a side note, planar binding does state that the duration is instantaneous however the spell usage and text suggests that there is more to it than this.

The creature can escape from the trap with by successfully pitting its spell resistance against your caster level check, by dimensional travel, or with a successful Charisma check (DC 15 + ½ your caster level + your Cha modifier). It can try each method once per day. If it breaks loose, it can flee or attack you. A dimensional anchor cast on the creature prevents its escape via dimensional travel. You can also employ a calling diagram (see magic circle against evil) to make the trap more secure.

If the creature does not break free of the trap, you can keep it bound for as long as you dare. You can attempt to compel the creature to perform a service by describing the service and perhaps offering some sort of reward. You make a Charisma check opposed by the creature’s Charisma check. The check is assigned a bonus of +0 to +6 based on the nature of the service and the reward. If the creature wins the opposed check, it refuses service. New offers, bribes, and the like can be made or the old ones reoffered every 24 hours. This process can be repeated until the creature promises to serve, until it breaks free, or until you decide to get rid of it by means of some other spell.

If you assign some open-ended task that the creature cannot complete though its own actions the spell remains in effect for a maximum of one day per caster level, and the creature gains an immediate chance to break free.

(Paraphrased). Given that they explicitly give it an instantaneous duration, I'd rule that the effect of the magic is only in the conjuration whereas the rest is left to roleplay. However, I've been in games where DMs ruled that the trap they were held in is magical and it seems this would apply in your airship example (I know nothing of that feat). It seemed reasonable enough to me, but then again that erinyes was just sitting there as opposed to causing a ship to fly. In this case I'd agree with Jonathan Drain's answer, that the effect is suppressed but the elemental's prison is not.